# Relay, Don't Route: Adaptive Population Handoff for Cost-Efficient LLM-Driven Evolution

arXiv: https://arxiv.org/abs/2608.05651 · HTML: https://mlsanity.com/paper/2608.05651/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [AdaEvolve: Adaptive LLM Driven Zeroth-Order Optimization](https://mlsanity.com/paper/2602.20133/) (2026)
- [CORAL: Towards Autonomous Multi-Agent Evolution for Open-Ended Discovery](https://mlsanity.com/paper/2604.01658/) (2026)
- [CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimization](https://mlsanity.com/paper/2510.14150/) (2025)
- [PACEvolve: Enabling Progress-Aware Consistent Evolution](https://mlsanity.com/paper/2601.10657/) (2026)
- [Cognitive Alpha Mining via LLM-Driven Code-Based Evolution](https://mlsanity.com/paper/2511.18850/) (2025)
- [Harness-Aware Self-Evolving: Co-Evolving Model Weights, Harness, and Task Solutions](https://mlsanity.com/paper/2607.03935/) (2026)
- [AdaptEvolve: Improving Efficiency of Evolutionary AI Agents through Adaptive Model Selection](https://mlsanity.com/paper/2602.11931/) (2026)
- [LEVI: Stronger Search Architectures Can Substitute for Larger LLMs in Evolutionary Search](https://mlsanity.com/paper/2605.09764/) (2026)
- [New Bounds for Zarankiewicz Numbers via Reinforced LLM Evolutionary Search](https://mlsanity.com/paper/2605.01120/) (2026)
- [SeaEvo: Advancing Algorithm Discovery with Strategy Space Evolution](https://mlsanity.com/paper/2604.24372/) (2026)

## Built on by (most cited first, 2 of 2)

- [Optimize Cheap, Deploy Strong: Cost-Aware Cross-Tier Transfer for Evolutionary Optimization](https://mlsanity.com/paper/2608.10694/) (2026)
- [Humanize MLE Agents: Multi-Agent Session Alternation Beyond Single-Agent Limits](https://mlsanity.com/paper/2610.13494/) (2026)

## Abstract (arXiv)

Large language model (LLM)-driven evolution has shown promise for program search and algorithm discovery, but relying on strong models throughout long evolutionary runs is costly. A natural alternative is to combine cheap and strong models under a fixed inference budget. However, existing approaches typically allocate models at the level of individual queries or mutation steps, overlooking that evolutionary search is textitstateful: each generated candidate changes the population from which subsequent mutations are produced. We empirically analyze LLM-driven evolutionary trajectories and find that search progress is strongly front-loaded, early trajectory performance is informative but noisy, and cheap models recover much of the early progress achieved by strong models at lower cost. Motivated by these findings, we propose model, a training-free framework that shifts budget allocation from individual calls to evolving populations through adaptive textitpopulation handoff. A cheap model explores multiple trajectories in short blocks allocated by a bandit scheduler. Relay Gain, defined as the marginal improvement of a compact, quality-diverse candidate bank constructed for handoff, serves as the scheduler reward and determines when to hand off. The curated candidates initialize a shared strong model population for refinement. Across four benchmarks and three budgets, model achieves the highest mean score in 11 of 12 settings, outperforming competitive baselines. Our results suggest that in stateful search, budget allocation should be organized around the population, not the individual call.